The general type of finite-part singular integrals and integral equations with logarithmic singularities used in fracture mechanics
type: Item
instance of: scholarly article
title: The general type of finite-part singular integrals and integral equations with logarithmic singularities used in fracture mechanics
zbMATH Open document ID: 0667.73072
DOI: 10.1007/BF01174641
author: E. G. Ladopoulos
published in: Acta Mechanica
publication date: 1988-01-01T00:00:00Z
review text: A new method is proposed, by using some special quadrature rules, for the numerical evaluation of the general type of finite-part singular integrals and integral equations with logarithmic singularities. In this way the system of such equations can be numerically solved by reduction to a system of linear equations. For this reduction, the singular integral equation is applied to a number of appropriately selected collocation points on the integration interval, and then a numerical integration rule is used for the approximation of the integrals in this equation. An application is given, to the determination of the intensity of the logarithmic singularity in a simple crack inside an infinite, isotropic solid.
Mathematics Subject Classification ID: 74R05
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45G05
Mathematics Subject Classification ID: 65D32
zbMATH DE Number: 4092946
zbMATH Keywords: integral equations of the first kind
zbMATH Keywords: Gauss method
zbMATH Keywords: Radau method
zbMATH Keywords: Lobatto method
zbMATH Keywords: quadrature rules
zbMATH Keywords: reduction to a system of linear equations
zbMATH Keywords: collocation points
zbMATH Keywords: intensity of the logarithmic singularity
zbMATH Keywords: infinite, isotropic solid
MaRDI profile type: Publication
cites work: On a new integration rule with the Gegenbauer polynomials for singular integral equations used in the theory of elasticity
cites work: On the numerical solution of the finite-part singular integral equations of the first and second kind used in fracture mechanics
cites work: Q3311636
cites work: Solution of plane anisotropic elastostatical boundary value problems by singular integral equations
cites work: Numerical Construction of Gaussian Quadrature Formulas for � � 1 0 &nbsp; (-Log x)⋅x α ⋅f(x) ⋅dx &nbsp;&nbsp;&nbsp; and &nbsp;&nbsp;&nbsp; � � ∞ 0 E m (x) ⋅f(x) ⋅dx
cites work: Q5790292
cites work: Cauchy-type integrals and integral equations with logarithmic singularities
cites work: Q5535928
cites work: Q5681646
cites work: Q5327757
cites work: Q5820804
Recommended article: On the numerical solution of the finite-part singular integral equations of the first and second kind used in fracture mechanics
Recommended article: Singular integral equations with two fixed singularities and applications to fractured composites
Recommended article: Hypersingular integral equations in fracture analysis
Recommended article: Q4309054
Recommended article: Q4208043
Recommended article: Q3175864
Recommended article: Hypersingular integrals in boundary element fracture analysis
Recommended article: Derivation of a new analytical solution for a general two‐dimensional finite‐part integral applicable in fracture mechanics
Recommended article: The singular function boundary integral method for a two-dimensional fracture problem
Recommended article: Closed-form solutions for finite-part integrals occurring in shear-mode fracture mechanics
description: scientific article; zbMATH DE number 4092946